text: The Mössbauer isomeric shift is the shift seen in gamma-ray spectroscopy when one compares two different nuclear isomeric states in two different physical, chemical or biological environments, and is due to the combined effect of the recoil-free Mössbauer transition between the two nuclear isomeric states and the transition between two atomic states in those two environments.
  The isomeric shift on atomic spectral lines depends on the electron wave function ψ and on the difference δφ of electrostatic potentials φ of the two isomeric states.
  For a given nuclear isomer in two different physical or chemical environments (different physical phases or different chemical combinations), the electron wave functions are also different. Therefore, on top of the isomeric shift on atomic spectral lines, which is due to the difference of the two nuclear isomer states, there will be a shift between the two environments (because of the experimental arrangement, these are called source (s) and absorber (a)). This combined shift is the Mössbauer isomeric shift, and it is described mathematically by the same formalism as the nuclear isomeric shift on atomic spectral lines, except that instead of one electron wave function, that in the source ψ, one deals with the difference between the electron wave function in the source ψ and the electron wave function in the absorber ψ:
  The first measurement of the isomeric shift in gamma spectroscopy with the help of the Mössbauer effect was reported in 1960, two years after its first experimental observation in atomic spectroscopy. By measuring this shift, one obtains important and extremely precise information, both about the nuclear isomer states and about the physical, chemical or biological environment of the atoms, represented by the electronic wave functions.
  Under its Mössbauer variant, the isomeric shift has found important applications in domains as different as atomic physics, solid-state physics, nuclear physics, chemistry, biology, metallurgy, mineralogy, geology, and lunar research. For further literature, see also.
  The nuclear isomeric shift has also been observed in muonic atoms, that is, atoms in which a muon is captured by the excited nucleus and makes a transition from an atomic excited state to the atomic ground state in a time shorter than the lifetime of the excited isomeric nuclear state.